A History of Science, Volume 1
by
Henry Smith Williams
Part 3 out of 5
close friend--in a sense the teacher--of Pericles and of
Euripides. Just how long he remained at Athens is not certain;
but the time came when he had made himself in some way
objectionable to the Athenian populace through his teachings.
Filled with the spirit of the investigator, he could not accept
the current conceptions as to the gods. He was a sceptic, an
innovator. Such men are never welcome; they are the chief factors
in the progress of thought, but they must look always to
posterity for recognition of their worth; from their
contemporaries they receive, not thanks, but persecution.
Sometimes this persecution takes one form, sometimes another; to
the credit of the Greeks be it said, that with them it usually
led to nothing more severe than banishment. In the case of
Anaxagoras, it is alleged that the sentence pronounced was death;
but that, thanks to the influence of Pericles, this sentence was
commuted to banishment. In any event, the aged philosopher was
sent away from the city of his adoption. He retired to Lampsacus.
"It is not I that have lost the Athenians," he said; "it is the
Athenians that have lost me."
The exact position which Anaxagoras had among his contemporaries,
and his exact place in the development of philosophy, have always
been somewhat in dispute. It is not known, of a certainty, that
he even held an open school at Athens. Ritter thinks it doubtful
that he did. It was his fate to be misunderstood, or
underestimated, by Aristotle; that in itself would have sufficed
greatly to dim his fame--might, indeed, have led to his almost
entire neglect had he not been a truly remarkable thinker. With
most of the questions that have exercised the commentators we
have but scant concern. Following Aristotle, most historians of
philosophy have been metaphysicians; they have concerned
themselves far less with what the ancient thinkers really knew
than with what they thought. A chance using of a verbal quibble,
an esoteric phrase, the expression of a vague mysticism--these
would suffice to call forth reams of exposition. It has been the
favorite pastime of historians to weave their own anachronistic
theories upon the scanty woof of the half- remembered thoughts of
the ancient philosophers. To make such cloth of the imagination
as this is an alluring pastime, but one that must not divert us
here. Our point of view reverses that of the philosophers. We are
chiefly concerned, not with some vague saying of Anaxagoras, but
with what he really knew regarding the phenomena of nature; with
what he observed, and with the comprehensible deductions that he
derived from his observations. In attempting to answer these
inquiries, we are obliged, in part, to take our evidence at
second-hand; but, fortunately, some fragments of writings of
Anaxagoras have come down to us. We are told that he wrote only a
single book. It was said even (by Diogenes) that he was the first
man that ever wrote a work in prose. The latter statement would
not bear too close an examination, yet it is true that no
extensive prose compositions of an earlier day than this have
been preserved, though numerous others are known by their
fragments. Herodotus, "the father of prose," was a slightly
younger contemporary of the Clazomenaean philosopher; not
unlikely the two men may have met at Athens.
Notwithstanding the loss of the greater part of the writings of
Anaxagoras, however, a tolerably precise account of his
scientific doctrines is accessible. Diogenes Laertius expresses
some of them in very clear and precise terms. We have already
pointed out the uncertainty that attaches to such evidence as
this, but it is as valid for Anaxagoras as for another. If we
reject such evidence, we shall often have almost nothing left; in
accepting it we may at least feel certain that we are viewing the
thinker as his contemporaries and immediate successors viewed
him. Following Diogenes, then, we shall find some remarkable
scientific opinions ascribed to Anaxagoras. "He asserted," we are
told, "that the sun was a mass of burning iron, greater than
Peloponnesus, and that the moon contained houses and also hills
and ravines." In corroboration of this, Plato represents him as
having conjectured the right explanation of the moon's light, and
of the solar and lunar eclipses. He had other astronomical
theories that were more fanciful; thus "he said that the stars
originally moved about in irregular confusion, so that at first
the pole-star, which is continually visible, always appeared in
the zenith, but that afterwards it acquired a certain
declination, and that the Milky Way was a reflection of the light
of the sun when the stars did not appear. The comets he
considered to be a concourse of planets emitting rays, and the
shooting- stars he thought were sparks, as it were, leaping from
the firmament."
Much of this is far enough from the truth, as we now know it, yet
all of it shows an earnest endeavor to explain the observed
phenomena of the heavens on rational principles. To have
predicated the sun as a great molten mass of iron was indeed a
wonderful anticipation of the results of the modern spectroscope.
Nor can it be said that this hypothesis of Anaxagoras was a
purely visionary guess. It was in all probability a scientific
deduction from the observed character of meteoric stones.
Reference has already been made to the alleged prediction of the
fall of the famous meteor at aegespotomi by Anaxagoras. The
assertion that he actually predicted this fall in any proper
sense of the word would be obviously absurd. Yet the fact that
his name is associated with it suggests that he had studied
similar meteorites, or else that he studied this particular one,
since it is not quite clear whether it was before or after this
fall that he made the famous assertion that space is full of
falling stones. We should stretch the probabilities were we to
assert that Anaxagoras knew that shooting-stars and meteors were
the same, yet there is an interesting suggestiveness in his
likening the shooting-stars to sparks leaping from the firmament,
taken in connection with his observation on meteorites. Be this
as it may, the fact that something which falls from heaven as a
blazing light turns out to be an iron-like mass may very well
have suggested to the most rational of thinkers that the great
blazing light called the sun has the same composition. This idea
grasped, it was a not unnatural extension to conceive the other
heavenly bodies as having the same composition.
This led to a truly startling thought. Since the heavenly bodies
are of the same composition as the earth, and since they are
observed to be whirling about the earth in space, may we not
suppose that they were once a part of the earth itself, and that
they have been thrown off by the force of a whirling motion? Such
was the conclusion which Anaxagoras reached; such his explanation
of the origin of the heavenly bodies. It was a marvellous guess.
Deduct from it all that recent science has shown to be untrue;
bear in mind that the stars are suns, compared with which the
earth is a mere speck of dust; recall that the sun is parent, not
daughter, of the earth, and despite all these deductions, the
cosmogonic guess of Anaxagoras remains, as it seems to us, one of
the most marvellous feats of human intelligence. It was the first
explanation of the cosmic bodies that could be called, in any
sense, an anticipation of what the science of our own day accepts
as a true explanation of cosmic origins. Moreover, let us urge
again that this was no mere accidental flight of the imagination;
it was a scientific induction based on the only data available;
perhaps it is not too much to say that it was the only scientific
induction which these data would fairly sustain. Of course it is
not for a moment to be inferred that Anaxagoras understood, in
the modern sense, the character of that whirling force which we
call centrifugal. About two thousand years were yet to elapse
before that force was explained as elementary inertia; and even
that explanation, let us not forget, merely sufficed to push back
the barriers of mystery by one other stage; for even in our day
inertia is a statement of fact rather than an explanation.
But however little Anaxagoras could explain the centrifugal force
on mechanical principles, the practical powers of that force were
sufficiently open to his observation. The mere experiment of
throwing a stone from a sling would, to an observing mind, be
full of suggestiveness. It would be obvious that by whirling the
sling about, the stone which it held would be sustained in its
circling path about the hand in seeming defiance of the earth's
pull, and after the stone had left the sling, it could fly away
from the earth to a distance which the most casual observation
would prove to be proportionate to the speed of its flight.
Extremely rapid motion, then, might project bodies from the
earth's surface off into space; a sufficiently rapid whirl would
keep them there. Anaxagoras conceived that this was precisely
what had occurred. His imagination even carried him a step
farther--to a conception of a slackening of speed, through which
the heavenly bodies would lose their centrifugal force, and,
responding to the perpetual pull of gravitation, would fall back
to the earth, just as the great stone at aegespotomi had been
observed to do.
Here we would seem to have a clear conception of the idea of
universal gravitation, and Anaxagoras stands before us as the
anticipator of Newton. Were it not for one scientific maxim, we
might exalt the old Greek above the greatest of modern natural
philosophers; but that maxim bids us pause. It is phrased thus,
"He discovers who proves." Anaxagoras could not prove; his
argument was at best suggestive, not demonstrative. He did not
even know the laws which govern falling bodies; much less could
he apply such laws, even had he known them, to sidereal bodies at
whose size and distance he could only guess in the vaguest terms.
Still his cosmogonic speculation remains as perhaps the most
remarkable one of antiquity. How widely his speculation found
currency among his immediate successors is instanced in a passage
from Plato, where Socrates is represented as scornfully answering
a calumniator in these terms: "He asserts that I say the sun is a
stone and the moon an earth. Do you think of accusing Anaxagoras,
Miletas, and have you so low an opinion of these men, and think
them so unskilled in laws, as not to know that the books of
Anaxagoras the Clazomenaean are full of these doctrines. And
forsooth the young men are learning these matters from me which
sometimes they can buy from the orchestra for a drachma, at the
most, and laugh at Socrates if he pretends they are
his-particularly seeing they are so strange."
The element of error contained in these cosmogonic speculations
of Anaxagoras has led critics to do them something less than
justice. But there is one other astronomical speculation for
which the Clazomenaean philosopher has received full credit. It
is generally admitted that it was he who first found out the
explanation of the phases of the moon; a knowledge that that body
shines only by reflected light, and that its visible forms,
waxing and waning month by month from crescent to disk and from
disk to crescent, merely represent our shifting view of its
sun-illumined face. It is difficult to put ourselves in the place
of the ancient observer and realize how little the appearances
suggest the actual fact. That a body of the same structure as the
earth should shine with the radiance of the moon merely because
sunlight is reflected from it, is in itself a supposition
seemingly contradicted by ordinary experience. It required the
mind of a philosopher, sustained, perhaps, by some experimental
observations, to conceive the idea that what seems so obviously
bright may be in reality dark. The germ of the conception of what
the philosopher speaks of as the noumena, or actualities, back of
phenomena or appearances, had perhaps this crude beginning.
Anaxagoras could surely point to the moon in support of his
seeming paradox that snow, being really composed of water, which
is dark, is in reality black and not white--a contention to which
we shall refer more at length in a moment.
But there is yet another striking thought connected with this new
explanation of the phases of the moon. The explanation implies
not merely the reflection of light by a dark body, but by a dark
body of a particular form. Granted that reflections are in
question, no body but a spherical one could give an appearance
which the moon presents. The moon, then, is not merely a mass of
earth, it is a spherical mass of earth. Here there were no flaws
in the reasoning of Anaxagoras. By scientific induction he passed
from observation to explanation. A new and most important element
was added to the science of astronomy.
Looking back from the latter-day stand-point, it would seem as if
the mind of the philosopher must have taken one other step: the
mind that had conceived sun, moon, stars, and earth to be of one
substance might naturally, we should think, have reached out to
the further induction that, since the moon is a sphere, the other
cosmic bodies, including the earth, must be spheres also. But
generalizer as he was, Anaxagoras was too rigidly scientific a
thinker to make this assumption. The data at his command did not,
as he analyzed them, seem to point to this conclusion. We have
seen that Pythagoras probably, and Parmenides surely, out there
in Italy had conceived the idea of the earth's rotundity, but the
Pythagorean doctrines were not rapidly taken up in the mother-
country, and Parmenides, it must be recalled, was a strict
contemporary of Anaxagoras himself. It is no reproach, therefore,
to the Clazomenaean philosopher that he should have held to the
old idea that the earth is flat, or at most a convex disk--the
latter being the Babylonian conception which probably dominated
that Milesian school to which Anaxagoras harked back.
Anaxagoras may never have seen an eclipse of the moon, and even
if he had he might have reflected that, from certain directions,
a disk may throw precisely the same shadow as a sphere. Moreover,
in reference to the shadow cast by the earth, there was, so
Anaxagoras believed, an observation open to him nightly which, we
may well suppose, was not without influence in suggesting to his
mind the probable shape of the earth. The Milky Way, which
doubtless had puzzled astronomers from the beginnings of history
and which was to continue to puzzle them for many centuries after
the day of Anaxagoras, was explained by the Clazomenaean
philosopher on a theory obviously suggested by the theory of the
moon's phases. Since the earth- like moon shines by reflected
light at night, and since the stars seem obviously brighter on
dark nights, Anaxagoras was but following up a perfectly logical
induction when he propounded the theory that the stars in the
Milky Way seem more numerous and brighter than those of any other
part of the heavens, merely because the Milky Way marks the
shadow of the earth. Of course the inference was wrong, so far as
the shadow of the earth is concerned; yet it contained a part
truth, the force of which was never fully recognized until the
time of Galileo. This consists in the assertion that the
brightness of the Milky Way is merely due to the glow of many
stars. The shadow- theory of Anaxagoras would naturally cease to
have validity so soon as the sphericity of the earth was proved,
and with it, seemingly, fell for the time the companion theory
that the Milky Way is made up of a multitude of stars.
It has been said by a modern critic[1] that the shadow-theory was
childish in that it failed to note that the Milky Way does not
follow the course of the ecliptic. But this criticism only holds
good so long as we reflect on the true character of the earth as
a symmetrical body poised in space. It is quite possible to
conceive a body occupying the position of the earth with
reference to the sun which would cast a shadow having such a
tenuous form as the Milky Way presents. Such a body obviously
would not be a globe, but a long-drawn-out, attenuated figure.
There is, to be sure, no direct evidence preserved to show that
Anaxagoras conceived the world to present such a figure as this,
but what we know of that philosopher's close-reasoning, logical
mind gives some warrant to the assumption--gratuitous though in a
sense it be-- that the author of the theory of the moon's phases
had not failed to ask himself what must be the form of that
terrestrial body which could cast the tenuous shadow of the Milky
Way. Moreover, we must recall that the habitable earth, as known
to the Greeks of that day, was a relatively narrow band of
territory, stretching far to the east and to the west.
Anaxagoras as Meteorologist
The man who had studied the meteorite of aegospotami, and been
put by it on the track of such remarkable inductions, was,
naturally, not oblivious to the other phenomena of the
atmosphere. Indeed, such a mind as that of Anaxagoras was sure to
investigate all manner of natural phenomena, and almost equally
sure to throw new light on any subject that it investigated.
Hence it is not surprising to find Anaxagoras credited with
explaining the winds as due to the rarefactions of the atmosphere
produced by the sun. This explanation gives Anaxagoras full right
to be called "the father of meteorology," a title which, it may
be, no one has thought of applying to him, chiefly because the
science of meteorology did not make its real beginnings until
some twenty-four hundred years after the death of its first great
votary. Not content with explaining the winds, this prototype of
Franklin turned his attention even to the tipper atmosphere.
"Thunder," he is reputed to have said, "was produced by the
collision of the clouds, and lightning by the rubbing together of
the clouds." We dare not go so far as to suggest that this
implies an association in the mind of Anaxagoras between the
friction of the clouds and the observed electrical effects
generated by the friction of such a substance as amber. To make
such a suggestion doubtless would be to fall victim to the old
familiar propensity to read into Homer things that Homer never
knew. Yet the significant fact remains that Anaxagoras ascribed
to thunder and to lightning their true position as strictly
natural phenomena. For him it was no god that menaced humanity
with thundering voice and the flash of his divine fires from the
clouds. Little wonder that the thinker whose science carried him
to such scepticism as this should have felt the wrath of the
superstitious Athenians.
Biological Speculations
Passing from the phenomena of the air to those of the earth
itself, we learn that Anaxagoras explained an earthquake as being
produced by the returning of air into the earth. We cannot be
sure as to the exact meaning here, though the idea that gases are
imprisoned in the substance of the earth seems not far afield.
But a far more remarkable insight than this would imply was shown
by Anaxagoras when he asserted that a certain amount of air is
contained in water, and that fishes breathe this air. The passage
of Aristotle in which this opinion is ascribed to Anaxagoras is
of sufficient interest to be quoted at length:
"Democritus, of Abdera," says Aristotle, "and some others, that
have spoken concerning respiration, have determined nothing
concerning other animals, but seem to have supposed that all
animals respire. But Anaxagoras and Diogenes (Apolloniates), who
say that all animals respire, have also endeavored to explain how
fishes, and all those animals that have a hard, rough shell, such
as oysters, mussels, etc., respire. And Anaxagoras, indeed, says
that fishes, when they emit water through their gills, attract
air from the mouth to the vacuum in the viscera from the water
which surrounds the mouth; as if air was inherent in the
water."[2]
It should be recalled that of the three philosophers thus
mentioned as contending that all animals respire, Anaxagoras was
the elder; he, therefore, was presumably the originator of the
idea. It will be observed, too, that Anaxagoras alone is held
responsible for the idea that fishes respire air through their
gills, "attracting" it from the water. This certainly was one of
the shrewdest physiological guesses of any age, if it be regarded
as a mere guess. With greater justice we might refer to it as a
profound deduction from the principle of the uniformity of
nature.
In making such a deduction, Anaxagoras was far in advance of his
time as illustrated by the fact that Aristotle makes the citation
we have just quoted merely to add that "such things are
impossible," and to refute these "impossible" ideas by means of
metaphysical reasonings that seemed demonstrative not merely to
himself, but to many generations of his followers.
We are told that Anaxagoras alleged that all animals were
originally generated out of moisture, heat, and earth particles.
Just what opinion he held concerning man's development we are not
informed. Yet there is one of his phrases which
suggests--without, perhaps, quite proving--that he was an
evolutionist. This phrase asserts, with insight that is fairly
startling, that man is the most intelligent of animals because he
has hands. The man who could make that assertion must, it would
seem, have had in mind the idea of the development of
intelligence through the use of hands-- an idea the full force of
which was not evident to subsequent generations of thinkers until
the time of Darwin.
Physical Speculations
Anaxagoras is cited by Aristotle as believing that "plants are
animals and feel pleasure and pain, inferring this because they
shed their leaves and let them grow again." The idea is fanciful,
yet it suggests again a truly philosophical conception of the
unity of nature. The man who could conceive that idea was but
little hampered by traditional conceptions. He was exercising a
rare combination of the rigidly scientific spirit with the
poetical imagination. He who possesses these gifts is sure not to
stop in his questionings of nature until he has found some
thinkable explanation of the character of matter itself.
Anaxagoras found such an explanation, and, as good luck would
have it, that explanation has been preserved. Let us examine his
reasoning in some detail. We have already referred to the claim
alleged to have been made by Anaxagoras that snow is not really
white, but black. The philosopher explained his paradox, we are
told, by asserting that snow is really water, and that water is
dark, when viewed under proper conditions--as at the bottom of a
well. That idea contains the germ of the Clazomenaean
philosopher's conception of the nature of matter. Indeed, it is
not unlikely that this theory of matter grew out of his
observation of the changing forms of water. He seems clearly to
have grasped the idea that snow on the one hand, and vapor on the
other, are of the same intimate substance as the water from which
they are derived and into which they may be again transformed.
The fact that steam and snow can be changed back into water, and
by simple manipulation cannot be changed into any other
substance, finds, as we now believe, its true explanation in the
fact that the molecular structure, as we phrase it--that is to
say, the ultimate particle of which water is composed, is not
changed, and this is precisely the explanation which Anaxagoras
gave of the same phenomena. For him the unit particle of water
constituted an elementary body, uncreated, unchangeable,
indestructible. This particle, in association with like
particles, constitutes the substance which we call water. The
same particle in association with particles unlike itself, might
produce totally different substances--as, for example, when water
is taken up by the roots of a plant and becomes, seemingly, a
part of the substance of the plant. But whatever the changed
association, so Anaxagoras reasoned, the ultimate particle of
water remains a particle of water still. And what was true of
water was true also, so he conceived, of every other substance.
Gold, silver, iron, earth, and the various vegetables and animal
tissues--in short, each and every one of all the different
substances with which experience makes us familiar, is made up of
unit particles which maintain their integrity in whatever
combination they may be associated. This implies, obviously, a
multitude of primordial particles, each one having an
individuality of its own; each one, like the particle of water
already cited, uncreated, unchangeable, and indestructible.
Fortunately, we have the philosopher's own words to guide us as
to his speculations here. The fragments of his writings that have
come down to us (chiefly through the quotations of Simplicius)
deal almost exclusively with these ultimate conceptions of his
imagination. In ascribing to him, then, this conception of
diverse, uncreated, primordial elements, which can never be
changed, but can only be mixed together to form substances of the
material world, we are not reading back post-Daltonian knowledge
into the system of Anaxagoras. Here are his words: "The Greeks do
not rightly use the terms 'coming into being' and 'perishing.'
For nothing comes into being, nor, yet, does anything perish; but
there is mixture and separation of things that are. So they would
do right in calling 'coming into being' 'mixture' and 'perishing'
'separation.' For how could hair come from what is not hair? Or
flesh from what is not flesh?"
Elsewhere he tells us that (at one stage of the world's
development) "the dense, the moist, the cold, the dark, collected
there where now is earth; the rare, the warm, the dry, the
bright, departed towards the further part of the aether. The
earth is condensed out of these things that are separated, for
water is separated from the clouds, and earth from the water; and
from the earth stones are condensed by the cold, and these are
separated farther from the water." Here again the influence of
heat and cold in determining physical qualities is kept
pre-eminently in mind. The dense, the moist, the cold, the dark
are contrasted with the rare, the warm, the dry, and bright; and
the formation of stones is spoken of as a specific condensation
due to the influence of cold. Here, then, we have nearly all the
elements of the Daltonian theory of atoms on the one hand, and
the nebular hypothesis of Laplace on the other. But this is not
quite all. In addition to such diverse elementary particles as
those of gold, water, and the rest, Anaxagoras conceived a
species of particles differing from all the others, not merely as
they differ from one another, but constituting a class by
themselves; particles infinitely smaller than the others;
particles that are described as infinite, self-powerful, mixed
with nothing, but existing alone. That is to say (interpreting
the theory in the only way that seems plausible), these most
minute particles do not mix with the other primordial particles
to form material substances in the same way in which these mixed
with one another. But, on the other hand, these "infinite,
self-powerful, and unmixed" particles commingle everywhere and in
every substance whatever with the mixed particles that go to make
up the substances.
There is a distinction here, it will be observed, which at once
suggests the modern distinction between physical processes and
chemical processes, or, putting it otherwise, between molecular
processes and atomic processes; but the reader must be guarded
against supposing that Anaxagoras had any such thought as this in
mind. His ultimate mixable particles can be compared only with
the Daltonian atom, not with the molecule of the modern
physicist, and his "infinite, self- powerful, and unmixable"
particles are not comparable with anything but the ether of the
modern physicist, with which hypothetical substance they have
many points of resemblance. But the "infinite, self- powerful,
and unmixed" particles constituting thus an ether-like plenum
which permeates all material structures, have also, in the mind
of Anaxagoras, a function which carries them perhaps a stage
beyond the province of the modern ether. For these "infinite,
self powerful, and unmixed" particles are imbued with, and,
indeed, themselves constitute, what Anaxagoras terms nous, a word
which the modern translator has usually paraphrased as "mind."
Neither that word nor any other available one probably conveys an
accurate idea of what Anaxagoras meant to imply by the word nous.
For him the word meant not merely "mind" in the sense of
receptive and comprehending intelligence, but directive and
creative intelligence as well. Again let Anaxagoras speak for
himself: "Other things include a portion of everything, but nous
is infinite, and self-powerful, and mixed with nothing, but it
exists alone, itself by itself. For if it were not by itself, but
were mixed with anything else, it would include parts of all
things, if it were mixed with anything; for a portion of
everything exists in every thing, as has been said by me before,
and things mingled with it would prevent it from having power
over anything in the same way that it does now that it is alone
by itself. For it is the most rarefied of all things and the
purest, and it has all knowledge in regard to everything and the
greatest power; over all that has life, both greater and less,
nous rules. And nous ruled the rotation of the whole, so that it
set it in rotation in the beginning. First it began the rotation
from a small beginning, then more and more was included in the
motion, and yet more will be included. Both the mixed and the
separated and distinct, all things nous recognized. And whatever
things were to be, and whatever things were, as many as are now,
and whatever things shall be, all these nous arranged in order;
and it arranged that rotation, according to which now rotate
stars and sun and moon and air and aether, now that they are
separated. Rotation itself caused the separation, and the dense
is separated from the rare, the warm from the cold, the bright
from the dark, the dry from the moist. And when nous began to set
things in motion, there was separation from everything that was
in motion, all this was made distinct. The rotation of the things
that were moved and made distinct caused them to be yet more
distinct."[3]
Nous, then, as Anaxagoras conceives it, is "the most rarefied of
all things, and the purest, and it has knowledge in regard to
everything and the greatest power; over all that has life, both
greater and less, it rules." But these are postulants of
omnipresence and omniscience. In other words, nous is nothing
less than the omnipotent artificer of the material universe. It
lacks nothing of the power of deity, save only that we are not
assured that it created the primordial particles. The creation of
these particles was a conception that for Anaxagoras, as for the
modern Spencer, lay beyond the range of imagination. Nous is the
artificer, working with "uncreated" particles. Back of nous and
the particles lies, for an Anaxagoras as for a Spencer, the
Unknowable. But nous itself is the equivalent of that universal
energy of motion which science recognizes as operating between
the particles of matter, and which the theologist personifies as
Deity. It is Pantheistic deity as Anaxagoras conceives it; his
may be called the first scientific conception of a non-
anthropomorphic god. In elaborating this conception Anaxagoras
proved himself one of the most remarkable scientific dreamers of
antiquity. To have substituted for the Greek Pantheon of
anthropomorphic deities the conception of a non-anthropomorphic
immaterial and ethereal entity, of all things in the world "the
most rarefied and the purest," is to have performed a feat which,
considering the age and the environment in which it was
accomplished, staggers the imagination. As a strictly scientific
accomplishment the great thinker's conception of primordial
elements contained a germ of the truth which was to lie dormant
for 2200 years, but which then, as modified and vitalized by the
genius of Dalton, was to dominate the new chemical science of the
nineteenth century. If there are intimations that the primordial
element of Anaxagoras and of Dalton may turn out in the near
future to be itself a compound, there will still remain the yet
finer particles of the nous of Anaxagoras to baffle the most
subtle analysis of which to-day's science gives us any
pre-vision. All in all, then, the work of Anaxagoras must stand
as that of perhaps the most far-seeing scientific imagination of
pre-Socratic antiquity.
LEUCIPPUS AND DEMOCRITUS
But we must not leave this alluring field of speculation as to
the nature of matter without referring to another scientific
guess, which soon followed that of Anaxagoras and was destined to
gain even wider fame, and which in modern times has been somewhat
unjustly held to eclipse the glory of the other achievement. We
mean, of course, the atomic theory of Leucippus and Democritus.
This theory reduced all matter to primordial elements, called
atoms because they are by hypothesis incapable of
further division. These atoms, making up the entire material
universe, are in this theory conceived as qualitatively
identical, differing from one another only in size and perhaps in
shape. The union of different-sized atoms in endless combinations
produces the diverse substances with which our senses make us
familiar.
Before we pass to a consideration of this alluring theory, and
particularly to a comparison of it with the theory of Anaxagoras,
we must catch a glimpse of the personality of the men to whom the
theory owes its origin. One of these, Leucippus, presents so
uncertain a figure as to be almost mythical. Indeed, it was long
questioned whether such a man had actually lived, or whether be
were not really an invention of his alleged disciple, Democritus.
Latterday scholarship, however, accepts him as a real personage,
though knowing scarcely more of him than that he was the author
of the famous theory with which his name was associated. It is
suggested that he was a wanderer, like most philosophers of his
time, and that later in life he came to Abdera, in Thrace, and
through this circumstance became the teacher of Democritus. This
fable answers as well as another. What we really know is that
Democritus himself, through whose writings and teachings the
atomic theory gained vogue, was born in Abdera, about the year
460 B.C.--that is to say, just about the time when his great
precursor, Anaxagoras, was migrating to Athens. Democritus, like
most others of the early Greek thinkers, lives in tradition as a
picturesque figure. It is vaguely reported that he travelled for
a time, perhaps in the East and in Egypt, and that then he
settled down to spend the remainder of his life in Abdera.
Whether or not he visited Athens in the course of his wanderings
we do not know. At Abdera he was revered as a sage, but his
influence upon the practical civilization of the time was not
marked. He was pre-eminently a dreamer and a writer. Like his
confreres of the epoch, he entered all fields of thought. He
wrote voluminously, but, unfortunately, his writings have, for
the most part, perished. The fables and traditions of a later day
asserted that Democritus had voluntarily put out his own eyes
that he might turn his thoughts inward with more concentration.
Doubtless this is fiction, yet, as usual with such fictions, it
contains a germ of truth; for we may well suppose that the
promulgator of the atomic theory was a man whose mind was
attracted by the subtleties of thought rather than by the
tangibilities of observation. Yet the term "laughing
philosopher," which seems to have been universally applied to
Democritus, suggests a mind not altogether withdrawn from the
world of practicalities.
So much for Democritus the man. Let us return now to his theory
of atoms. This theory, it must be confessed, made no very great
impression upon his contemporaries. It found an expositor, a
little later, in the philosopher Epicurus, and later still the
poet Lucretius gave it popular expression. But it seemed scarcely
more than the dream of a philosopher or the vagary of a poet
until the day when modern science began to penetrate the
mysteries of matter. When, finally, the researches of Dalton and
his followers had placed the atomic theory on a surer footing as
the foundation of modern chemistry, the ideas of the old laughing
philosopher of Abdera, which all along had been half derisively
remembered, were recalled with a new interest. Now it appeared
that these ideas had curiously foreshadowed nineteenth-century
knowledge. It appeared that away back in the fifth century B.C. a
man had dreamed out a conception of the ultimate nature of matter
which had waited all these centuries for corroboration. And now
the historians of philosophy became more than anxious to do
justice to the memory of Democritus.
It is possible that this effort at poetical restitution has
carried the enthusiast too far. There is, indeed, a curious
suggestiveness in the theory of Democritus; there is
philosophical allurement in his reduction of all matter to a
single element; it contains, it may be, not merely a germ of the
science of the nineteenth-century chemistry, but perhaps the
germs also of the yet undeveloped chemistry of the twentieth
century. Yet we dare suggest that in their enthusiasm for the
atomic theory of Democritus the historians of our generation have
done something less than justice to that philosopher's precursor,
Anaxagoras. And one suspects that the mere accident of a name has
been instrumental in producing this result. Democritus called his
primordial element an atom; Anaxagoras, too, conceived a
primordial element, but he called it merely a seed or thing; he
failed to christen it distinctively. Modern science adopted the
word atom and gave it universal vogue. It owed a debt of
gratitude to Democritus for supplying it the word, but it
somewhat overpaid the debt in too closely linking the new meaning
of the word with its old original one. For, let it be clearly
understood, the Daltonian atom is not precisely comparable with
the atom of Democritus. The atom, as Democritus conceived it, was
monistic; all atoms, according to this hypothesis, are of the
same substance; one atom differs from another merely in size and
shape, but not at all in quality. But the Daltonian hypothesis
conceived, and nearly all the experimental efforts of the
nineteenth century seemed to prove, that there are numerous
classes of atoms, each differing in its very essence from the
others.
As the case stands to-day the chemist deals with seventy-odd
substances, which he calls elements. Each one of these substances
is, as he conceives it, made up of elementary atoms having a
unique personality, each differing in quality from all the
others. As far as experiment has thus far safely carried us, the
atom of gold is a primordial element which remains an atom of
gold and nothing else, no matter with what other atoms it is
associated. So, too, of the atom of silver, or zinc, or
sodium--in short, of each and every one of the seventy-odd
elements. There are, indeed, as we shall see, experiments that
suggest the dissolution of the atom--that suggest, in short, that
the Daltonian atom is misnamed, being a structure that may, under
certain conditions, be broken asunder. But these experiments
have, as yet, the warrant rather of philosophy than of pure
science, and to-day we demand that the philosophy of science
shall be the handmaid of experiment.
When experiment shall have demonstrated that the Daltonian atom
is a compound, and that in truth there is but a single true atom,
which, combining with its fellows perhaps in varying numbers and
in different special relations, produces the Daltonian atoms,
then the philosophical theory of monism will have the
experimental warrant which to-day it lacks; then we shall be a
step nearer to the atom of Democritus in one direction, a step
farther away in the other. We shall be nearer, in that the
conception of Democritus was, in a sense, monistic; farther away,
in that all the atoms of Democritus, large and small alike, were
considered as permanently fixed in size. Democritus postulated
all his atoms as of the same substance, differing not at all in
quality; yet he was obliged to conceive that the varying size of
the atoms gave to them varying functions which amounted to
qualitative differences. He might claim for his largest atom the
same quality of substance as for his smallest, but so long as he
conceived that the large atoms, when adjusted together to form a
tangible substance, formed a substance different in quality from
the substance which the small atoms would make up when similarly
grouped, this concession amounts to the predication of difference
of quality between the atoms themselves. The entire question
reduces itself virtually to a quibble over the word quality, So
long as one atom conceived to be primordial and indivisible is
conceded to be of such a nature as necessarily to produce a
different impression on our senses, when grouped with its
fellows, from the impression produced by other atoms when
similarly grouped, such primordial atoms do differ among
themselves in precisely the same way for all practical purposes
as do the primordial elements of Anaxagoras.
The monistic conception towards which twentieth- century
chemistry seems to be carrying us may perhaps show that all the
so-called atoms are compounded of a single element. All the true
atoms making up that element may then properly be said to have
the same quality, but none the less will it remain true that the
combinations of that element that go to make up the different
Daltonian atoms differ from one another in quality in precisely
the same sense in which such tangible substances as gold, and
oxygen, and mercury, and diamonds differ from one another. In the
last analysis of the monistic philosophy, there is but one
substance and one quality in the universe. In the widest view of
that philosophy, gold and oxygen and mercury and diamonds are one
substance, and, if you please, one quality. But such refinements
of analysis as this are for the transcendental philosopher, and
not for the scientist. Whatever the allurement of such reasoning,
we must for the purpose of science let words have a specific
meaning, nor must we let a mere word-jugglery blind us to the
evidence of facts. That was the rock on which Greek science
foundered; it is the rock which the modern helmsman sometimes
finds it difficult to avoid. And if we mistake not, this case of
the atom of Democritus is precisely a case in point. Because
Democritus said that his atoms did not differ in quality, the
modern philosopher has seen in his theory the essentials of
monism; has discovered in it not merely a forecast of the
chemistry of the nineteenth century, but a forecast of the
hypothetical chemistry of the future. And, on the other hand,
because Anaxagoras predicted a different quality for his
primordial elements, the philosopher of our day has discredited
the primordial element of Anaxagoras.
Yet if our analysis does not lead us astray, the theory of
Democritus was not truly monistic; his indestructible atoms,
differing from one another in size and shape, utterly incapable
of being changed from the form which they had maintained from the
beginning, were in reality as truly and primordially different as
are the primordial elements of Anaxagoras. In other words, the
atom of Democritus is nothing less than the primordial seed of
Anaxagoras, a little more tangibly visualized and given a
distinctive name. Anaxagoras explicitly conceived his elements as
invisibly small, as infinite in number, and as made up of an
indefinite number of kinds--one for each distinctive substance in
the world. But precisely the same postulates are made of the atom
of Democritus. These also are invisibly small; these also are
infinite in number; these also are made up of an indefinite
number of kinds, corresponding with the observed difference of
substances in the world. "Primitive seeds," or "atoms," were
alike conceived to be primordial, un- changeable, and
indestructible. Wherein then lies the difference? We answer,
chiefly in a name; almost solely in the fact that Anaxagoras did
not attempt to postulate the physical properties of the elements
beyond stating that each has a distinctive personality, while
Democritus did attempt to postulate these properties. He, too,
admitted that each kind of element has its distinctive
personality, and he attempted to visualize and describe the
characteristics of the personality.
Thus while Anaxagoras tells us nothing of his elements except
that they differ from one another, Democritus postulates a
difference in size, imagines some elements as heavier and some as
lighter, and conceives even that the elements may be provided
with projecting hooks, with the aid of which they link themselves
one with another. No one to-day takes these crude visualizings
seriously as to their details. The sole element of truth which
these dreamings contain, as distinguishing them from the
dreamings of Anaxagoras, is in the conception that the various
atoms differ in size and weight. Here, indeed, is a vague
fore-shadowing of that chemistry of form which began to come into
prominence towards the close of the nineteenth century. To have
forecast even dimly this newest phase of chemical knowledge,
across the abyss of centuries, is indeed a feat to put Democritus
in the front rank of thinkers. But this estimate should not blind
us to the fact that the pre-vision of Democritus was but a slight
elaboration of a theory which had its origin with another
thinker. The association between Anaxagoras and Democritus cannot
be directly traced, but it is an association which the historian
of ideas should never for a moment forget. If we are not to be
misled by mere word-jugglery, we shall recognize the founder of
the atomic theory of matter in Anaxagoras; its expositors along
slightly different lines in Leucippus and Democritus; its
re-discoverer of the nineteenth century in Dalton. All in all,
then, just as Anaxagoras preceded Democritus in time, so must he
take precedence over him also as an inductive thinker, who
carried the use of the scientific imagination to its farthest
reach.
An analysis of the theories of the two men leads to somewhat the
same conclusion that might be reached from a comparison of their
lives. Anaxagoras was a sceptical, experimental scientist, gifted
also with the prophetic imagination. He reasoned always from the
particular to the general, after the manner of true induction,
and he scarcely took a step beyond the confines of secure
induction. True scientist that he was, he could content himself
with postulating different qualities for his elements, without
pretending to know how these qualities could be defined. His
elements were by hypothesis invisible, hence he would not attempt
to visualize them. Democritus, on the other hand, refused to
recognize this barrier. Where he could not know, he still did not
hesitate to guess. Just as he conceived his atom of a definite
form with a definite structure, even so he conceived that the
atmosphere about him was full of invisible spirits; he accepted
the current superstitions of his time. Like the average Greeks of
his day, he even believed in such omens as those furnished by
inspecting the entrails of a fowl. These chance bits of biography
are weather- vanes of the mind of Democritus. They tend to
substantiate our conviction that Democritus must rank below
Anaxagoras as a devotee of pure science. But, after all, such
comparisons and estimates as this are utterly futile. The
essential fact for us is that here, in the fifth century before
our era, we find put forward the most penetrating guess as to the
constitution of matter that the history of ancient thought has to
present to us. In one direction, the avenue of progress is
barred; there will be no farther step that way till we come down
the centuries to the time of Dalton.
HIPPOCRATES AND GREEK MEDICINE
These studies of the constitution of matter have carried us to
the limits of the field of scientific imagination in antiquity;
let us now turn sharply and consider a department of science in
which theory joins hands with practicality. Let us witness the
beginnings of scientific therapeutics.
Medicine among the early Greeks, before the time of Hippocrates,
was a crude mixture of religion, necromancy, and mysticism.
Temples were erected to the god of medicine, aesculapius, and
sick persons made their way, or were carried, to these temples,
where they sought to gain the favor of the god by suitable
offerings, and learn the way to regain their health through
remedies or methods revealed to them in dreams by the god. When
the patient had been thus cured, he placed a tablet in the temple
describing his sickness, and telling by what method the god had
cured him. He again made suitable offerings at the temple, which
were sometimes in the form of gold or silver representations of
the diseased organ--a gold or silver model of a heart, hand,
foot, etc.
Nevertheless, despite this belief in the supernatural, many drugs
and healing lotions were employed, and the Greek physicians
possessed considerable skill in dressing wounds and bandaging.
But they did not depend upon these surgical dressings alone,
using with them certain appropriate prayers and incantations,
recited over the injured member at the time of applying the
dressings.
Even the very early Greeks had learned something of anatomy. The
daily contact with wounds and broken bones must of necessity lead
to a crude understanding of anatomy in general. The first Greek
anatomist, however, who is recognized as such, is said to have
been Alcmaeon. He is said to have made extensive dissections of
the lower animals, and to have described many hitherto unknown
structures, such as the optic nerve and the Eustachian canal--the
small tube leading into the throat from the ear. He is credited
with many unique explanations of natural phenomena, such as, for
example, the explanation that "hearing is produced by the hollow
bone behind the ear; for all hollow things are sonorous." He was
a rationalist, and he taught that the brain is the organ of mind.
The sources of our information about his work, however, are
unreliable.
Democedes, who lived in the sixth century B.C., is the first
physician of whom we have any trustworthy history. We learn from
Herodotus that he came from Croton to aegina, where, in
recognition of his skill, he was appointed medical officer of the
city. From aegina he was called to Athens at an increased salary,
and later was in charge of medical affairs in several other Greek
cities. He was finally called to Samos by the tyrant Polycrates,
who reigned there from about 536 to 522 B.C. But on the death of
Polycrates, who was murdered by the Persians, Democedes became a
slave. His fame as a physician, however, had reached the ears of
the Persian monarch, and shortly after his capture he was
permitted to show his skill upon King Darius himself. The Persian
monarch was suffering from a sprained ankle, which his Egyptian
surgeons had been unable to cure. Democedes not only cured the
injured member but used his influence in saving the lives of his
Egyptian rivals, who had been condemned to death by the king.
At another time he showed his skill by curing the queen, who was
suffering from a chronic abscess of long standing. This so
pleased the monarch that he offered him as a reward anything he
might desire, except his liberty. But the costly gifts of Darius
did not satisfy him so long as he remained a slave; and
determined to secure his freedom at any cost, he volunteered to
lead some Persian spies into his native country, promising to use
his influence in converting some of the leading men of his nation
to the Persian cause. Laden with the wealth that had been heaped
upon him by Darius, he set forth upon his mission, but upon
reaching his native city of Croton he threw off his mask,
renounced his Persian mission, and became once more a free Greek.
While the story of Democedes throws little light upon the medical
practices of the time, it shows that paid city medical officers
existed in Greece as early as the fifth and sixth centuries B.C.
Even then there were different "schools" of medicine, whose
disciples disagreed radically in their methods of treating
diseases; and there were also specialists in certain diseases,
quacks, and charlatans. Some physicians depended entirely upon
external lotions for healing all disorders; others were
"hydrotherapeutists" or "bath- physicians"; while there were a
host of physicians who administered a great variety of herbs and
drugs. There were also magicians who pretended to heal by
sorcery, and great numbers of bone-setters, oculists, and
dentists.
Many of the wealthy physicians had hospitals, or clinics, where
patients were operated upon and treated. They were not hospitals
in our modern understanding of the term, but were more like
dispensaries, where patients were treated temporarily, but were
not allowed to remain for any length of time. Certain communities
established and supported these dispensaries for the care of the
poor.
But anything approaching a rational system of medicine was not
established, until Hippocrates of Cos, the "father of medicine,"
came upon the scene. In an age that produced Phidias, Lysias,
Herodotus, Sophocles, and Pericles, it seems but natural that the
medical art should find an exponent who would rise above
superstitious dogmas and lay the foundation for a medical
science. His rejection of the supernatural alone stamps the
greatness of his genius. But, besides this, he introduced more
detailed observation of diseases, and demonstrated the importance
that attaches to prognosis.
Hippocrates was born at Cos, about 460 B.C., but spent most of
his life at Larissa, in Thessaly. He was educated as a physician
by his father, and travelled extensively as an itinerant
practitioner for several years. His travels in different climates
and among many different people undoubtedly tended to sharpen his
keen sense of observation. He was a practical physician as well
as a theorist, and, withal, a clear and concise writer. "Life is
short," he says, "opportunity fleeting, judgment difficult,
treatment easy, but treatment after thought is proper and
profitable."
His knowledge of anatomy was necessarily very imperfect, and was
gained largely from his predecessors, to whom he gave full
credit. Dissections of the human body were forbidden him, and he
was obliged to confine his experimental researches to operations
on the lower animals. His knowledge of the structure and
arrangement of the bones, however, was fairly accurate, but the
anatomy of the softer tissues, as he conceived it, was a queer
jumbling together of blood-vessels, muscles, and tendons. He does
refer to "nerves," to be sure, but apparently the structures
referred to are the tendons and ligaments, rather than the nerves
themselves. He was better acquainted with the principal organs in
the cavities of the body, and knew, for example, that the heart
is divided into four cavities, two of which he supposed to
contain blood, and the other two air.
His most revolutionary step was his divorcing of the supernatural
from the natural, and establishing the fact that disease is due
to natural causes and should be treated accordingly. The effect
of such an attitude can hardly be over-estimated. The
establishment of such a theory was naturally followed by a close
observation as to the course of diseases and the effects of
treatment. To facilitate this, he introduced the custom of
writing down his observations as he made them--the "clinical
history" of the case. Such clinical records are in use all over
the world to-day, and their importance is so obvious that it is
almost incomprehensible that they should have fallen into disuse
shortly after the time of Hippocrates, and not brought into
general use again until almost two thousand years later.
But scarcely less important than his recognition of disease as a
natural phenomenon was the importance he attributed to prognosis.
Prognosis, in the sense of prophecy, was common before the time
of Hippocrates. But prognosis, as he practised it and as we
understand it to-day, is prophecy based on careful observation of
the course of diseases--something more than superstitious
conjecture.
Although Hippocratic medicine rested on the belief in natural
causes, nevertheless, dogma and theory held an important place.
The humoral theory of disease was an all-important one, and so
fully was this theory accepted that it influenced the science of
medicine all through succeeding centuries. According to this
celebrated theory there are four humors in the body-- blood,
phlegm, yellow bile, and black bile. When these humors are mixed
in exact proportions they constitute health; but any deviations
from these proportions produce disease. In treating diseases the
aim of the physician was to discover which of these humors were
out of proportion and to restore them to their natural
equilibrium. It was in the methods employed in this restitution,
rather than a disagreement about the humors themselves, that
resulted in the various "schools" of medicine.
In many ways the surgery of Hippocrates showed a better
understanding of the structure of the organs than of their
functions. Some of the surgical procedures as described by him
are followed, with slight modifications, to-day. Many of his
methods were entirely lost sight of until modern times, and one,
the treatment of dislocation of the outer end of the collar-bone,
was not revived until some time in the eighteenth century.
Hippocrates, it seems, like modern physicians, sometimes suffered
from the ingratitude of his patients. "The physician visits a
patient suffering from fever or a wound, and prescribes for him,"
he says; "on the next day, if the patient feels worse the blame
is laid upon the physician; if, on the other hand, he feels
better, nature is extolled, and the physician reaps no praise."
The essence of this has been repeated in rhyme and prose by
writers in every age and country, but the "father of medicine"
cautions physicians against allowing it to influence their
attitude towards their profession.
VIII. POST-SOCRATIC SCIENCE AT ATHENS--PLATO, ARISTOTLE, AND
THEOPHRASTUS
Doubtless it has been noticed that our earlier scientists were as
far removed as possible from the limitations of specialism. In
point of fact, in this early day, knowledge had not been
classified as it came to be later on. The philosopher was, as his
name implied, a lover of knowledge, and he did not find it beyond
the reach of his capacity to apply himself to all departments of
the field of human investigation. It is nothing strange to
discover that Anaximander and the Pythagoreans and Anaxagoras
have propounded theories regarding the structure of the cosmos,
the origin and development of animals and man, and the nature of
matter itself. Nowadays, so enormously involved has become the
mass of mere facts regarding each of these departments of
knowledge that no one man has the temerity to attempt to master
them all. But it was different in those days of beginnings. Then
the methods of observation were still crude, and it was quite the
custom for a thinker of forceful personality to find an eager
following among disciples who never thought of putting his
theories to the test of experiment. The great lesson that true
science in the last resort depends upon observation and
measurement, upon compass and balance, had not yet been learned,
though here and there a thinker like Anaxagoras had gained an
inkling of it.
For the moment, indeed, there in Attica, which was now, thanks to
that outburst of Periclean culture, the centre of the world's
civilization, the trend of thought was to take quite another
direction. The very year which saw the birth of Democritus at
Abdera, and of Hippocrates, marked also the birth, at Athens, of
another remarkable man, whose influence it would scarcely be
possible to over-estimate. This man was Socrates. The main facts
of his history are familiar to every one. It will be recalled
that Socrates spent his entire life in Athens, mingling
everywhere with the populace; haranguing, so the tradition goes,
every one who would listen; inculcating moral lessons, and
finally incurring the disapprobation of at least a voting
majority of his fellow-citizens. He gathered about him a company
of remarkable men with Plato at their head, but this could not
save him from the disapprobation of the multitudes, at whose
hands he suffered death, legally administered after a public
trial. The facts at command as to certain customs of the Greeks
at this period make it possible to raise a question as to whether
the alleged "corruption of youth," with which Socrates was
charged, may not have had a different implication from what
posterity has preferred to ascribe to it. But this thought,
almost shocking to the modern mind and seeming altogether
sacrilegious to most students of Greek philosophy, need not here
detain us; neither have we much concern in the present connection
with any part of the teaching of the martyred philosopher. For
the historian of metaphysics, Socrates marks an epoch, but for
the historian of science he is a much less consequential figure.
Similarly regarding Plato, the aristocratic Athenian who sat at
the feet of Socrates, and through whose writings the teachings of
the master found widest currency. Some students of philosophy
find in Plato "the greatest thinker and writer of all time."[1]
The student of science must recognize in him a thinker whose
point of view was essentially non-scientific; one who tended
always to reason from the general to the particular rather than
from the particular to the general. Plato's writings covered
almost the entire field of thought, and his ideas were presented
with such literary charm that successive generations of readers
turned to them with unflagging interest, and gave them wide
currency through copies that finally preserved them to our own
time. Thus we are not obliged in his case, as we are in the case
of every other Greek philosopher, to estimate his teachings
largely from hearsay evidence. Plato himself speaks to us
directly. It is true, the literary form which he always adopted,
namely, the dialogue, does not give quite the same certainty as
to when he is expressing his own opinions that a more direct
narrative would have given; yet, in the main, there is little
doubt as to the tenor of his own opinions--except, indeed, such
doubt as always attaches to the philosophical reasoning of the
abstract thinker.
What is chiefly significant from our present standpoint is that
the great ethical teacher had no significant message to give the
world regarding the physical sciences. He apparently had no
sharply defined opinions as to the mechanism of the universe; no
clear conception as to the origin or development of organic
beings; no tangible ideas as to the problems of physics; no
favorite dreams as to the nature of matter. Virtually his back
was turned on this entire field of thought. He was under the sway
of those innate ideas which, as we have urged, were among the
earliest inductions of science. But he never for a moment
suspected such an origin for these ideas. He supposed his
conceptions of being, his standards of ethics, to lie back of all
experience; for him they were the most fundamental and most
dependable of facts. He criticised Anaxagoras for having tended
to deduce general laws from observation. As we moderns see it,
such criticism is the highest possible praise. It is a criticism
that marks the distinction between the scientist who is also a
philosopher and the philosopher who has but a vague notion of
physical science. Plato seemed, indeed, to realize the value of
scientific investigation; he referred to the astronomical studies
of the Egyptians and Chaldeans, and spoke hopefully of the
results that might accrue were such studies to be taken up by
that Greek mind which, as he justly conceived, had the power to
vitalize and enrich all that it touched. But he told here of what
he would have others do, not of what he himself thought of doing.
His voice was prophetic, but it stimulated no worker of his own
time.
Plato himself had travelled widely. It is a familiar legend that
he lived for years in Egypt, endeavoring there to penetrate the
mysteries of Egyptian science. It is said even that the rudiments
of geometry which he acquired there influenced all his later
teachings. But be that as it may, the historian of science must
recognize in the founder of the Academy a moral teacher and
metaphysical dreamer and sociologist, but not, in the modern
acceptance of the term, a scientist. Those wider phases of
biological science which find their expression in metaphysics, in
ethics, in political economy, lie without our present scope; and
for the development of those subjects with which we are more
directly concerned, Plato, like his master, has a negative
significance.
ARISTOTLE (384-322 B.C.)
When we pass to that third great Athenian teacher, Aristotle, the
case is far different. Here was a man whose name was to be
received as almost a synonym for Greek science for more than a
thousand years after his death. All through the Middle Ages his
writings were to be accepted as virtually the last word regarding
the problems of nature. We shall see that his followers actually
preferred his mandate to the testimony of their own senses. We
shall see, further, that modern science progressed somewhat in
proportion as it overthrew the Aristotelian dogmas. But the
traditions of seventeen or eighteen centuries are not easily set
aside, and it is perhaps not too much to say that the name of
Aristotle stands, even in our own time, as vaguely representative
in the popular mind of all that was highest and best in the
science of antiquity. Yet, perhaps, it would not be going too far
to assert that something like a reversal of this judgment would
be nearer the truth. Aristotle did, indeed, bring together a
great mass of facts regarding animals in his work on natural
history, which, being preserved, has been deemed to entitle its
author to be called the "father of zoology." But there is no
reason to suppose that any considerable portion of this work
contained matter that was novel, or recorded observations that
were original with Aristotle; and the classifications there
outlined are at best but a vague foreshadowing of the elaboration
of the science. Such as it is, however, the natural history
stands to the credit of the Stagirite. He must be credited, too,
with a clear enunciation of one most important scientific
doctrine--namely, the doctrine of the spherical figure of the
earth. We have already seen that this theory originated with the
Pythagorean philosophers out in Italy. We have seen, too, that
the doctrine had not made its way in Attica in the time of
Anaxagoras. But in the intervening century it had gained wide
currency, else so essentially conservative a thinker as Aristotle
would scarcely have accepted it. He did accept it, however, and
gave the doctrine clearest and most precise expression. Here are
his words:[2]
"As to the figure of the earth it must necessarily be
spherical.... If it were not so, the eclipses of the moon would
not have such sections as they have. For in the configurations in
the course of a month the deficient part takes all different
shapes; it is straight, and concave, and convex; but in eclipses
it always has the line of divisions convex; wherefore, since the
moon is eclipsed in consequence of the interposition of the
earth, the periphery of the earth must be the cause of this by
having a spherical form. And again, from the appearance of the
stars it is clear, not only that the earth is round, but that its
size is not very large; for when we make a small removal to the
south or the north, the circle of the horizon becomes palpably
different, so that the stars overhead undergo a great change, and
are not the same to those that travel in the north and to the
south. For some stars are seen in Egypt or at Cyprus, but are not
seen in the countries to the north of these; and the stars that
in the north are visible while they make a complete circuit,
there undergo a setting. So that from this it is manifest, not
only that the form of the earth is round, but also that it is a
part of a not very large sphere; for otherwise the difference
would not be so obvious to persons making so small a change of
place. Wherefore we may judge that those persons who connect the
region in the neighborhood of the pillars of Hercules with that
towards India, and who assert that in this way the sea is one, do
not assert things very improbable. They confirm this conjecture
moreover by the elephants, which are said to be of the same
species towards each extreme; as if this circumstance was a
consequence of the conjunction of the extremes. The
mathematicians who try to calculate the measure of the
circumference, make it amount to four hundred thousand stadia;
whence we collect that the earth is not only spherical, but is
not large compared with the magnitude of the other stars."
But in giving full meed of praise to Aristotle for the
promulgation of this doctrine of the sphericity of the earth, it
must unfortunately be added that the conservative philosopher
paused without taking one other important step. He could not
accept, but, on the contrary, he expressly repudiated, the
doctrine of the earth's motion. We have seen that this idea also
was a part of the Pythagorean doctrine, and we shall have
occasion to dwell more at length on this point in a succeeding
chapter. It has even been contended by some critics that it was
the adverse conviction of the Peripatetic philosopher which, more
than any other single influence, tended to retard the progress of
the true doctrine regarding the mechanism of the heavens.
Aristotle accepted the sphericity of the earth, and that doctrine
became a commonplace of scientific knowledge, and so continued
throughout classical antiquity. But Aristotle rejected the
doctrine of the earth's motion, and that doctrine, though
promulgated actively by a few contemporaries and immediate
successors of the Stagirite, was then doomed to sink out of view
for more than a thousand years. If it be a correct assumption
that the influence of Aristotle was, in a large measure,
responsible for this result, then we shall perhaps not be far
astray in assuming that the great founder of the Peripatetic
school was, on the whole, more instrumental in retarding the
progress of astronomical science that any other one man that ever
lived.
The field of science in which Aristotle was pre-eminently a
pathfinder is zoology. His writings on natural history have
largely been preserved, and they constitute by far the most
important contribution to the subject that has come down to us
from antiquity. They show us that Aristotle had gained possession
of the widest range of facts regarding the animal kingdom, and,
what is far more important, had attempted to classify these
facts. In so doing he became the founder of systematic zoology.
Aristotle's classification of the animal kingdom was known and
studied throughout the Middle Ages, and, in fact, remained in
vogue until superseded by that of Cuvier in the nineteenth
century. It is not to be supposed that all the terms of
Aristotle's classification originated with him. Some of the
divisions are too patent to have escaped the observation of his
predecessors. Thus, for example, the distinction between birds
and fishes as separate classes of animals is so obvious that it
must appeal to a child or to a savage. But the efforts of
Aristotle extended, as we shall see, to less patent
generalizations. At the very outset, his grand division of the
animal kingdom into blood-bearing and bloodless animals implies a
very broad and philosophical conception of the entire animal
kingdom. The modern physiologist does not accept the
classification, inasmuch as it is now known that colorless fluids
perform the functions of blood for all the lower organisms. But
the fact remains that Aristotle's grand divisions correspond to
the grand divisions of the Lamarckian system--vertebrates and
invertebrates-- which every one now accepts. Aristotle, as we
have said, based his classification upon observation of the
blood; Lamarck was guided by a study of the skeleton. The fact
that such diverse points of view could direct the observer
towards the same result gives, inferentially, a suggestive lesson
in what the modern physiologist calls the homologies of parts of
the organism.
Aristotle divides his so-called blood-bearing animals into five
classes: (1) Four-footed animals that bring forth their young
alive; (2) birds; (3) egg-laying four- footed animals (including
what modern naturalists call reptiles and amphibians); (4) whales
and their allies; (5) fishes. This classification, as will be
observed, is not so very far afield from the modern divisions
into mammals, birds, reptiles, amphibians, and fishes. That
Aristotle should have recognized the fundamental distinction
between fishes and the fish- like whales, dolphins, and porpoises
proves the far from superficial character of his studies.
Aristotle knew that these animals breathe by means of lungs and
that they produce living young. He recognized, therefore, their
affinity with his first class of animals, even if he did not,
like the modern naturalist, consider these affinities close
enough to justify bringing the two types together into a single
class.
The bloodless animals were also divided by Aristotle into five
classes--namely: (1) Cephalopoda (the octopus, cuttle-fish,
etc.); (2) weak-shelled animals (crabs, etc.); (3) insects and
their allies (including various forms, such as spiders and
centipedes, which the modern classifier prefers to place by
themselves); (4) hard-shelled animals (clams, oysters, snails,
etc.); (5) a conglomerate group of marine forms, including
star-fish, sea-urchins, and various anomalous forms that were
regarded as linking the animal to the vegetable worlds. This
classification of the lower forms of animal life continued in
vogue until Cuvier substituted for it his famous grouping into
articulates, mollusks, and radiates; which grouping in turn was
in part superseded later in the nineteenth century.
What Aristotle did for the animal kingdom his pupil,
Theophrastus, did in some measure for the vegetable kingdom.
Theophrastus, however, was much less a classifier than his
master, and his work on botany, called The Natural History of
Development, pays comparatively slight attention to theoretical
questions. It deals largely with such practicalities as the
making of charcoal, of pitch, and of resin, and the effects of
various plants on the animal organism when taken as foods or as
medicines. In this regard the work of Theophrastus, is more
nearly akin to the natural history of the famous Roman compiler,
Pliny. It remained, however, throughout antiquity as the most
important work on its subject, and it entitles Theophrastus to be
called the "father of botany." Theophrastus deals also with the
mineral kingdom after much the same fashion, and here again his
work is the most notable that was produced in antiquity.
IX. GREEK SCIENCE OF THE ALEXANDRIAN OR HELLENISTIC PERIOD
We are entering now upon the most important scientific epoch of
antiquity. When Aristotle and Theophrastus passed from the scene,
Athens ceased to be in any sense the scientific centre of the
world. That city still retained its reminiscent glory, and cannot
be ignored in the history of culture, but no great scientific
leader was ever again to be born or to take up his permanent
abode within the confines of Greece proper. With almost
cataclysmic suddenness, a new intellectual centre appeared on the
south shore of the Mediterranean. This was the city of
Alexandria, a city which Alexander the Great had founded during
his brief visit to Egypt, and which became the capital of Ptolemy
Soter when he chose Egypt as his portion of the dismembered
empire of the great Macedonian. Ptolemy had been with his master
in the East, and was with him in Babylonia when he died. He had
therefore come personally in contact with Babylonian
civilization, and we cannot doubt that this had a most important
influence upon his life, and through him upon the new
civilization of the West. In point of culture, Alexandria must be
regarded as the successor of Babylon, scarcely less directly than
of Greece. Following the Babylonian model, Ptolemy erected a
great museum and began collecting a library. Before his death it
was said that he had collected no fewer than two hundred thousand
manuscripts. He had gathered also a company of great teachers and
founded a school of science which, as has just been said, made
Alexandria the culture-centre of the world.
Athens in the day of her prime had known nothing quite like this.
Such private citizens as Aristotle are known to have had
libraries, but there were no great public collections of books in
Athens, or in any other part of the Greek domain, until Ptolemy
founded his famous library. As is well known, such libraries had
existed in Babylonia for thousands of years. The character which
the Ptolemaic epoch took on was no doubt due to Babylonian
influence, but quite as much to the personal experience of
Ptolemy himself as an explorer in the Far East. The marvellous
conquering journey of Alexander had enormously widened the
horizon of the Greek geographer, and stimulated the imagination
of all ranks of the people, It was but natural, then, that
geography and its parent science astronomy should occupy the
attention of the best minds in this succeeding epoch. In point of
fact, such a company of star-gazers and earth-measurers came upon
the scene in this third century B.C. as had never before existed
anywhere in the world. The whole trend of the time was towards
mechanics. It was as if the greatest thinkers had squarely faced
about from the attitude of the mystical philosophers of the
preceding century, and had set themselves the task of solving all
the mechanical riddles of the universe, They no longer troubled
themselves about problems of "being" and "becoming"; they gave
but little heed to metaphysical subtleties; they demanded that
their thoughts should be gauged by objective realities. Hence
there arose a succession of great geometers, and their
conceptions were applied to the construction of new mechanical
contrivances on the one hand, and to the elaboration of theories
of sidereal mechanics on the other.
The wonderful company of men who performed the feats that are
about to be recorded did not all find their home in Alexandria,
to be sure; but they all came more or less under the Alexandrian
influence. We shall see that there are two other important
centres; one out in Sicily, almost at the confines of the Greek
territory in the west; the other in Asia Minor, notably on the
island of Samos--the island which, it will be recalled, was at an
earlier day the birthplace of Pythagoras. But whereas in the
previous century colonists from the confines of the civilized
world came to Athens, now all eyes turned towards Alexandria, and
so improved were the facilities for communication that no doubt
the discoveries of one coterie of workers were known to all the
others much more quickly than had ever been possible before. We
learn, for example, that the studies of Aristarchus of Samos were
definitely known to Archimedes of Syracuse, out in Sicily.
Indeed, as we shall see, it is through a chance reference
preserved in one of the writings of Archimedes that one of the
most important speculations of Aristarchus is made known to us.
This illustrates sufficiently the intercommunication through
which the thought of the Alexandrian epoch was brought into a
single channel. We no longer, as in the day of the earlier
schools of Greek philosophy, have isolated groups of thinkers.
The scientific drama is now played out upon a single stage; and
if we pass, as we shall in the present chapter, from Alexandria
to Syracuse and from Syracuse to Samos, the shift of scenes does
no violence to the dramatic unities.
Notwithstanding the number of great workers who were not properly
Alexandrians, none the less the epoch is with propriety termed
Alexandrian. Not merely in the third century B.C., but throughout
the lapse of at least four succeeding centuries, the city of
Alexander and the Ptolemies continued to hold its place as the
undisputed culture-centre of the world. During that period Rome
rose to its pinnacle of glory and began to decline, without ever
challenging the intellectual supremacy of the Egyptian city. We
shall see, in a later chapter, that the Alexandrian influences
were passed on to the Mohammedan conquerors, and every one is
aware that when Alexandria was finally overthrown its place was
taken by another Greek city, Byzantium or Constantinople. But
that transfer did not occur until Alexandria had enjoyed a longer
period of supremacy as an intellectual centre than had perhaps
ever before been granted to any city, with the possible
exception of Babylon.
EUCLID (ABOUT 300 B.C.)
Our present concern is with that first wonderful development of
scientific activity which began under the first Ptolemy, and
which presents, in the course of the first century of Alexandrian
influence, the most remarkable coterie of scientific workers and
thinkers that antiquity produced. The earliest group of these new
leaders in science had at its head a man whose name has been a
household word ever since. This was Euclid, the father of
systematic geometry. Tradition has preserved to us but little of
the personality of this remarkable teacher; but, on the other
hand, his most important work has come down to us in its
entirety. The Elements of Geometry, with which the name of Euclid
is associated in the mind of every school-boy, presented the
chief propositions of its subject in so simple and logical a form
that the work remained a textbook everywhere for more than two
thousand years. Indeed it is only now beginning to be superseded.
It is not twenty years since English mathematicians could deplore
the fact that, despite certain rather obvious defects of the work
of Euclid, no better textbook than this was available. Euclid's
work, of course, gives expression to much knowledge that did not
originate with him. We have already seen that several important
propositions of geometry had been developed by Thales, and one by
Pythagoras, and that the rudiments of the subject were at least
as old as Egyptian civilization. Precisely how much Euclid added
through his own investigations cannot be ascertained. It seems
probable that he was a diffuser of knowledge rather than an
originator, but as a great teacher his fame is secure. He is
credited with an epigram which in itself might insure him
perpetuity of fame: "There is no royal road to geometry," was his
answer to Ptolemy when that ruler had questioned whether the
Elements might not be simplified. Doubtless this, like most
similar good sayings, is apocryphal; but whoever invented it has
made the world his debtor.
HEROPHILUS AND ERASISTRATUS
The catholicity of Ptolemy's tastes led him, naturally enough, to
cultivate the biological no less than the physical sciences. In
particular his influence permitted an epochal advance in the
field of medicine. Two anatomists became famous through the
investigations they were permitted to make under the patronage of
the enlightened ruler. These earliest of really scientific
investigators of the mechanism of the human body were named
Herophilus and Erasistratus. These two anatomists gained their
knowledge by the dissection of human bodies (theirs are the first
records that we have of such practices), and King Ptolemy himself
is said to have been present at some of these dissections. They
were the first to discover that the nerve- trunks have their
origin in the brain and spinal cord, and they are credited also
with the discovery that these nerve-trunks are of two different
kinds--one to convey motor, and the other sensory impulses. They
discovered, described, and named the coverings of the brain. The
name of Herophilus is still applied by anatomists, in honor of
the discoverer, to one of the sinuses or large canals that convey
the venous blood from the head. Herophilus also noticed and
described four cavities or ventricles in the brain, and reached
the conclusion that one of these ventricles was the seat of the
soul--a belief shared until comparatively recent times by many
physiologists. He made also a careful and fairly accurate study
of the anatomy of the eye, a greatly improved the old operation
for cataract.
With the increased knowledge of anatomy came also corresponding
advances in surgery, and many experimental operations are said to
have been performed upon condemned criminals who were handed over
to the surgeons by the Ptolemies. While many modern writers have
attempted to discredit these assertions, it is not improbable
that such operations were performed. In an age when human life
was held so cheap, and among a people accustomed to torturing
condemned prisoners for comparatively slight offences, it is not
unlikely that the surgeons were allowed to inflict perhaps less
painful tortures in the cause of science. Furthermore, we know
that condemned criminals were sometimes handed over to the
medical profession to be "operated upon and killed in whatever
way they thought best" even as late as the sixteenth century.
Tertullian[1] probably exaggerates, however, when he puts the
number of such victims in Alexandria at six hundred.
Had Herophilus and Erasistratus been as happy in their deductions
as to the functions of the organs as they were in their knowledge
of anatomy, the science of medicine would have been placed upon a
very high plane even in their time. Unfortunately, however, they
not only drew erroneous inferences as to the functions of the
organs, but also disagreed radically as to what functions certain
organs performed, and how diseases should be treated, even when
agreeing perfectly on the subject of anatomy itself. Their
contribution to the knowledge of the scientific treatment of
diseases holds no such place, therefore, as their anatomical
investigations.
Half a century after the time of Herophilus there appeared a
Greek physician, Heraclides, whose reputation in the use of drugs
far surpasses that of the anatomists of the Alexandrian school.
His reputation has been handed down through the centuries as that
of a physician, rather than a surgeon, although in his own time
he was considered one of the great surgeons of the period.
Heraclides belonged to the "Empiric" school, which rejected
anatomy as useless, depending entirely on the use of drugs. He is
thought to have been the first physician to point out the value
of opium in certain painful diseases. His prescription of this
drug for certain cases of "sleeplessness, spasm, cholera, and
colic," shows that his use of it was not unlike that of the
modern physician in certain cases; and his treatment of fevers,
by keeping the patient's head cool and facilitating the
secretions of the body, is still recognized as "good practice."
He advocated a free use of liquids in quenching the fever
patient's thirst--a recognized therapeutic measure to-day, but
one that was widely condemned a century ago.
ARCHIMEDES OF SYRACUSE AND THE FOUNDATION OF MECHANICS
We do not know just when Euclid died, but as he was at the height
of his fame in the time of Ptolemy I., whose reign ended in the
year 285 B.C., it is hardly probable that he was still living
when a young man named Archimedes came to Alexandria to study.
Archimedes was born in the Greek colony of Syracuse, on the
island of Sicily, in the year 287 B.C. When he visited Alexandria
he probably found Apollonius of Perga, the pupil of Euclid, at
the head of the mathematical school there. Just how long
Archimedes remained at Alexandria is not known. When he had
satisfied his curiosity or completed his studies, he returned to
Syracuse and spent his life there, chiefly under the patronage of
King Hiero, who seems fully to have appreciated his abilities.
Archimedes was primarily a mathematician. Left to his own
devices, he would probably have devoted his entire time to the
study of geometrical problems. But King Hiero had discovered that
his protege had wonderful mechanical ingenuity, and he made good
use of this discovery. Under stress of the king's urgings, the
philosopher was led to invent a great variety of mechanical
contrivances, some of them most curious ones. Antiquity credited
him with the invention of more than forty machines, and it is
these, rather than his purely mathematical discoveries, that gave
his name popular vogue both among his contemporaries and with
posterity. Every one has heard of the screw of Archimedes,
through which the paradoxical effect was produced of making water
seem to flow up hill. The best idea of this curious mechanism is
obtained if one will take in hand an ordinary corkscrew, and
imagine this instrument to be changed into a hollow tube,
retaining precisely the same shape but increased to some feet in
length and to a proportionate diameter. If one will hold the
corkscrew in a slanting direction and turn it slowly to the
right, supposing that the point dips up a portion of water each
time it revolves, one can in imagination follow the flow of that
portion of water from spiral to spiral, the water always running
downward, of course, yet paradoxically being lifted higher and
higher towards the base of the corkscrew, until finally it pours
out (in the actual Archimedes' tube) at the top. There is another
form of the screw in which a revolving spiral blade operates
within a cylinder, but the principle is precisely the same. With
either form water may be lifted, by the mere turning of the
screw, to any desired height. The ingenious mechanism excited the
wonder of the contemporaries of Archimedes, as well it might.
More efficient devices have superseded it in modern times, but it
still excites the admiration of all who examine it, and its
effects seem as paradoxical as ever.
Some other of the mechanisms of Archimedes have been made known
to successive generations of readers through the pages of
Polybius and Plutarch. These are the devices through which
Archimedes aided King Hiero to ward off the attacks of the Roman
general Marcellus, who in the course of the second Punic war laid
siege to Syracuse.
Plutarch, in his life of Marcellus, describes the Roman's attack
and Archimedes' defence in much detail. Incidentally he tells us
also how Archimedes came to make the devices that rendered the
siege so famous:
"Marcellus himself, with threescore galleys of five rowers at
every bank, well armed and full of all sorts of artillery and
fireworks, did assault by sea, and rowed hard to the wall, having
made a great engine and device of battery, upon eight galleys
chained together, to batter the wall: trusting in the great
multitude of his engines of battery, and to all such other
necessary provision as he had for wars, as also in his own
reputation. But Archimedes made light account of all his devices,
as indeed they were nothing comparable to the engines himself had
invented. This inventive art to frame instruments and engines
(which are called mechanical, or organical, so highly commended
and esteemed of all sorts of people) was first set forth by
Architas, and by Eudoxus: partly to beautify a little the science
of geometry by this fineness, and partly to prove and confirm by
material examples and sensible instruments, certain geometrical
conclusions, where of a man cannot find out the conceivable
demonstrations by enforced reasons and proofs. As that conclusion
which instructeth one to search out two lines mean proportional,
which cannot be proved by reason demonstrative, and yet
notwithstanding is a principle and an accepted ground for many
things which are contained in the art of portraiture. Both of
them have fashioned it to the workmanship of certain instruments,
called mesolabes or mesographs, which serve to find these mean
lines proportional, by drawing certain curve lines, and
overthwart and oblique sections. But after that Plato was
offended with them, and maintained against them, that they did
utterly corrupt and disgrace, the worthiness and excellence of
geometry, making it to descend from things not comprehensible and
without body, unto things sensible and material, and to bring it
to a palpable substance, where the vile and base handiwork of man
is to be employed: since that time, I say, handicraft, or the art
of engines, came to be separated from geometry, and being long
time despised by the philosophers, it came to be one of the
warlike arts.
"But Archimedes having told King Hiero, his kinsman and friend,
that it was possible to remove as great a weight as he would,
with as little strength as he listed to put to it: and boasting
himself thus (as they report of him) and trusting to the force of
his reasons, wherewith he proved this conclusion, that if there
were another globe of earth, he was able to remove this of ours,
and pass it over to the other: King Hiero wondering to hear him,
required him to put his device in execution, and to make him see
by experience, some great or heavy weight removed, by little
force. So Archimedes caught hold with a book of one of the
greatest carects, or hulks of the king (that to draw it to the
shore out of the water required a marvellous number of people to
go about it, and was hardly to be done so) and put a great number
of men more into her, than her ordinary burden: and he himself
sitting alone at his ease far off, without any straining at all,
drawing the end of an engine with many wheels and pulleys, fair
and softly with his hand, made it come as gently and smoothly to
him, as it had floated in the sea. The king wondering to see the
sight, and knowing by proof the greatness of his art; be prayed
him to make him some engines, both to assault and defend, in all
manner of sieges and assaults. So Archimedes made him many
engines, but King Hiero never occupied any of them, because he
reigned the most part of his time in peace without any wars. But
this provision and munition of engines, served the Syracusan's
turn marvellously at that time: and not only the provision of the
engines ready made, but also the engineer and work-master
himself, that had invented them.
"Now the Syracusans, seeing themselves assaulted by the Romans,
both by sea and by land, were marvellously perplexed, and could
not tell what to say, they were so afraid: imagining it was
impossible for them to withstand so great an army. But when
Archimedes fell to handling his engines, and to set them at
liberty, there flew in the air infinite kinds of shot, and
marvellous great stones, with an incredible noise and force on
the sudden, upon the footmen that came to assault the city by
land, bearing down, and tearing in pieces all those which came
against them, or in what place soever they lighted, no earthly
body being able to resist the violence of so heavy a weight: so
that all their ranks were marvellously disordered. And as for the
galleys that gave assault by sea, some were sunk with long pieces
of timber like unto the yards of ships, whereto they fasten their
sails, which were suddenly blown over the walls with force of
their engines into their galleys, and so sunk them by their over
great weight."
Polybius describes what was perhaps the most important of these
contrivances, which was, he tells us, "a band of iron, hanging by
a chain from the beak of a machine, which was used in the
following manner. The person who, like a pilot, guided the beak,
having let fall the hand, and catched hold of the prow of any
vessel, drew down the opposite end of the machine that was on the
inside of the walls. And when the vessel was thus raised erect
upon its stem, the machine itself was held immovable; but, the
chain being suddenly loosened from the beak by the means of
pulleys, some of the vessels were thrown upon their sides, others
turned with the bottom upwards; and the greatest part, as the
prows were plunged from a considerable height into the sea, were
filled with water, and all that were on board thrown into tumult
and disorder.
"Marcellus was in no small degree embarrassed," Polybius
continues, "when he found himself encountered in every attempt by
such resistance. He perceived that all his efforts were defeated
with loss; and were even derided by the enemy. But, amidst all
the anxiety that he suffered, he could not help jesting upon the
inventions of Archimedes. This man, said he, employs our ships as
buckets to draw water: and boxing about our sackbuts, as if they
were unworthy to be associated with him, drives them from his
company with disgrace. Such was the success of the siege on the
side of the sea."
Subsequently, however, Marcellus took the city by strategy, and
Archimedes was killed, contrary, it is said, to the express
orders of Marcellus. "Syracuse being taken," says Plutarch,
"nothing grieved Marcellus more than the loss of Archimedes. Who,
being in his study when the city was taken, busily seeking out by
himself the demonstration of some geometrical proposition which
he had drawn in figure, and so earnestly occupied therein, as he
neither saw nor heard any noise of enemies that ran up and down
the city, and much less knew it was taken: he wondered when he
saw a soldier by him, that bade him go with him to Marcellus.
Notwithstanding, he spake to the soldier, and bade him tarry
until he had done his conclusion, and brought it to
demonstration: but the soldier being angry with his answer, drew
out his sword and killed him. Others say, that the Roman soldier
when he came, offered the sword's point to him, to kill him: and
that Archimedes when he saw him, prayed him to hold his hand a
little, that he might not leave the matter he looked for
imperfect, without demonstration. But the soldier making no
reckoning of his speculation, killed him presently. It is
reported a third way also, saying that certain soldiers met him
in the streets going to Marcellus, carrying certain mathematical
instruments in a little pretty coffer, as dials for the sun,
spheres, and angles, wherewith they measure the greatness of the
body of the sun by view: and they supposing he had carried some
gold or silver, or other precious jewels in that little coffer,
slew him for it. But it is most certain that Marcellus was
marvellously sorry for his death, and ever after hated the
villain that slew him, as a cursed and execrable person: and how
he had made also marvellous much afterwards of Archimedes'
kinsmen for his sake."
We are further indebted to Plutarch for a summary of the
character and influence of Archimedes, and for an interesting
suggestion as to the estimate which the great philosopher put
upon the relative importance of his own discoveries.
"Notwithstanding Archimedes had such a great mind, and was so
profoundly learned, having hidden in him the only treasure and
secrets of geometrical inventions: as be would never set forth
any book how to make all these warlike engines, which won him at
that time the fame and glory, not of man's knowledge, but rather
of divine wisdom. But he esteeming all kind of handicraft and
invention to make engines, and generally all manner of sciences
bringing common commodity by the use of them, to be but vile,
beggarly, and mercenary dross: employed his wit and study only to
write things, the beauty and subtlety whereof were not mingled
anything at all with necessity. For all that he hath written, are
geometrical propositions, which are without comparison of any
other writings whatsoever: because the subject where of they
treat, doth appear by demonstration, the maker gives them the
grace and the greatness, and the demonstration proving it so
exquisitely, with wonderful reason and facility, as it is not
repugnable. For in all geometry are not to be found more profound
and difficult matters written, in more plain and simple terms,
and by more easy principles, than those which he hath invented.
Now some do impute this, to the sharpness of his wit and
understanding, which was a natural gift in him: others do refer
it to the extreme pains he took, which made these things come so
easily from him, that they seemed as if they had been no trouble
to him at all. For no man living of himself can devise the
demonstration of his propositions, what pains soever he take to
seek it: and yet straight so soon as he cometh to declare and
open it, every man then imagineth with himself he could have
found it out well enough, he can then so plainly make
demonstration of the thing he meaneth to show. And therefore that
methinks is likely to be true, which they write of him: that he
was so ravished and drunk with the sweet enticements of this
siren, which as it were lay continually with him, as he forgot
his meat and drink, and was careless otherwise of himself, that
oftentimes his servants got him against his will to the baths to
wash and anoint him: and yet being there, he would ever be
drawing out of the geometrical figures, even in the very imbers
of the chimney. And while they were anointing of him with oils
and sweet savours, with his finger he did draw lines upon his
naked body: so far was he taken from himself, and brought into an
ecstasy or trance, with the delight he had in the study of
geometry, and truly ravished with the love of the Muses. But
amongst many notable things he devised, it appeareth, that he
most esteemed the demonstration of the proportion between the
cylinder (to wit, the round column) and the sphere or globe
contained in the same: for he prayed his kinsmen and friends,
that after his death they would put a cylinder upon his tomb,
containing a massy sphere, with an inscription of the proportion,
whereof the continent exceedeth the thing contained."[2]
It should be observed that neither Polybius nor Plutarch mentions
the use of burning-glasses in connection with the siege of
Syracuse, nor indeed are these referred to by any other ancient
writer of authority. Nevertheless, a story gained credence down
to a late day to the effect that Archimedes had set fire to the
fleet of the enemy with the aid of concave mirrors. An experiment
was made by Sir Isaac Newton to show the possibility of a
phenomenon so well in accord with the genius of Archimedes, but
the silence of all the early authorities makes it more than
doubtful whether any such expedient was really adopted.
It will be observed that the chief principle involved in all
these mechanisms was a capacity to transmit great power through
levers and pulleys, and this brings us to the most important
field of the Syracusan philosopher's activity. It was as a
student of the lever and the pulley that Archimedes was led to
some of his greatest mechanical discoveries. He is even credited
with being the discoverer of the compound pulley. More likely he
was its developer only, since the principle of the pulley was
known to the old Babylonians, as their sculptures testify. But
there is no reason to doubt the general outlines of the story
that Archimedes astounded King Hiero by proving that, with the
aid of multiple pulleys, the strength of one man could suffice to
drag the largest ship from its moorings.
The property of the lever, from its fundamental principle, was
studied by him, beginning with the self- evident fact that "equal
bodies at the ends of the equal arms of a rod, supported on its
middle point, will balance each other"; or, what amounts to the
same thing stated in another way, a regular cylinder of uniform
matter will balance at its middle point. From this starting-point
he elaborated the subject on such clear and satisfactory
principles that they stand to-day practically unchanged and with
few additions. From all his studies and experiments he finally
formulated the principle that "bodies will be in equilibrio when
their distance from the fulcrum or point of support is inversely
as their weight." He is credited with having summed up his
estimate of the capabilities of the lever with the well-known
expression, "Give me a fulcrum on which to rest or a place on
which to stand, and I will move the earth."
But perhaps the feat of all others that most appealed to the
imagination of his contemporaries, and possibly also the one that
had the greatest bearing upon the position of Archimedes as a
scientific discoverer, was the one made familiar through the tale
of the crown of Hiero. This crown, so the story goes, was
supposed to be made of solid gold, but King Hiero for some reason
suspected the honesty of the jeweller, and desired to know if
Archimedes could devise a way of testing the question without
injuring the crown. Greek imagination seldom spoiled a story in
the telling, and in this case the tale was allowed to take on the
most picturesque of phases. The philosopher, we are assured,
pondered the problem for a long time without succeeding, but one
day as he stepped into a bath, his attention was attracted by the
overflow of water. A new train of ideas was started in his
ever-receptive brain. Wild with enthusiasm he sprang from the
bath, and, forgetting his robe, dashed along the streets of
Syracuse, shouting: "Eureka! Eureka!" (I have found it!) The
thought that had come into his mind was this: That any heavy
substance must have a bulk proportionate to its weight; that gold
and silver differ in weight, bulk for bulk, and that the way to
test the bulk of such an irregular object as a crown was to
immerse it in water. The experiment was made. A lump of pure gold
of the weight of the crown was immersed in a certain receptacle
filled with water, and the overflow noted. Then a lump of pure
silver of the same weight was similarly immersed; lastly the
crown itself was immersed, and of course--for the story must not
lack its dramatic sequel--was found bulkier than its weight of
pure gold. Thus the genius that could balk warriors and armies
could also foil the wiles of the silversmith.
Whatever the truth of this picturesque narrative, the fact
remains that some, such experiments as these must have paved the
way for perhaps the greatest of all the studies of
Archimedes--those that relate to the buoyancy of water. Leaving
the field of fable, we must now examine these with some
precision. Fortunately, the writings of Archimedes himself are
still extant, in which the results of his remarkable experiments
are related, so we may present the results in the words of the
discoverer.
Here they are: "First: The surface of every coherent liquid in a
state of rest is spherical, and the centre of the sphere
coincides with the centre of the earth. Second: A solid body
which, bulk for bulk, is of the same weight as a liquid, if
immersed in the liquid will sink so that the surface of the body
is even with the surface of the liquid, but will not sink deeper.
Third: Any solid body which is lighter, bulk for bulk, than a
liquid, if placed in the liquid will sink so deep as to displace
the mass of liquid equal in weight to another body. Fourth: If a
body which is lighter than a liquid is forcibly immersed in the
liquid, it will be pressed upward with a force corresponding to
the weight of a like volume of water, less the weight of the body
itself. Fifth: Solid bodies which, bulk for bulk, are heavier
than a liquid, when immersed in the liquid sink to the bottom,
but become in the liquid as much lighter as the weight of the
displaced water itself differs from the weight of the solid."
These propositions are not difficult to demonstrate, once they
are conceived, but their discovery, combined with the discovery
of the laws of statics already referred to, may justly be
considered as proving Archimedes the most inventive experimenter
of antiquity.
Curiously enough, the discovery which Archimedes himself is said
to have considered the most important of all his innovations is
one that seems much less striking. It is the answer to the
question, What is the relation in bulk between a sphere and its
circumscribing cylinder? Archimedes finds that the ratio is
simply two to three. We are not informed as to how he reached his
conclusion, but an obvious method would be to immerse a ball in a
cylindrical cup. The experiment is one which any one can make for
himself, with approximate accuracy, with the aid of a tumbler and
a solid rubber ball or a billiard-ball of just the right size.
Another geometrical problem which Archimedes solved was the
problem as to the size of a triangle which has equal area with a
circle; the answer being, a triangle having for its base the
circumference of the circle and for its altitude the radius.
Archimedes solved also the problem of the relation of the
diameter of the circle to its circumference; his answer being a
close approximation to the familiar 3.1416, which every tyro in
geometry will recall as the equivalent of pi.
Numerous other of the studies of Archimedes having reference to
conic sections, properties of curves and spirals, and the like,
are too technical to be detailed here. The extent of his
mathematical knowledge, however, is suggested by the fact that he
computed in great detail the number of grains of sand that would
be required to cover the sphere of the sun's orbit, making
certain hypothetical assumptions as to the size of the earth and
the distance of the sun for the purposes of argument.
Mathematicians find his computation peculiarly interesting
because it evidences a crude conception of the idea of
logarithms. From our present stand-point, the paper in which this
calculation is contained has considerable interest because of its
assumptions as to celestial mechanics. Thus Archimedes starts out
with the preliminary assumption that the circumference of the
earth is less than three million stadia. It must be understood
that this assumption is purely for the sake of argument.
Archimedes expressly states that he takes this number because it
is "ten times as large as the earth has been supposed to be by
certain investigators." Here, perhaps, the reference is to
Eratosthenes, whose measurement of the earth we shall have
occasion to revert to in a moment. Continuing, Archimedes asserts
that the sun is larger than the earth, and the earth larger than
the moon. In this assumption, he says, he is following the
opinion of the majority of astronomers. In the third place,
Archimedes assumes that the diameter of the sun is not more than
thirty times greater than that of the moon. Here he is probably
basing his argument upon another set of measurements of
Aristarchus, to which, also, we shall presently refer more at
length. In reality, his assumption is very far from the truth,
since the actual diameter of the sun, as we now know, is
something like four hundred times that of the moon. Fourth, the
circumference of the sun is greater than one side of the
thousand- faced figure inscribed in its orbit. The measurement,
it is expressly stated, is based on the measurements of
Aristarchus, who makes the diameter of the sun 1/170 of its
orbit. Archimedes adds, however, that he himself has measured the
angle and that it appears to him to be less than 1/164, and
greater than 1/200 part of the orbit. That is to say, reduced to
modern terminology, he places the limit of the sun's apparent
size between thirty-three minutes and twenty-seven minutes of
arc. As the real diameter is thirty-two minutes, this calculation
is surprisingly exact, considering the implements then at
command. But the honor of first making it must be given to
Aristarchus and not to Archimedes.
We need not follow Archimedes to the limits of his
incomprehensible numbers of sand-grains. The calculation is
chiefly remarkable because it was made before the introduction of
the so-called Arabic numerals had simplified mathematical
calculations. It will be recalled that the Greeks used letters
for numerals, and, having no cipher, they soon found themselves
in difficulties when large numbers were involved. The Roman
system of numerals simplified the matter somewhat, but the
beautiful simplicity of the decimal system did not come into
vogue until the Middle Ages, as we shall see. Notwithstanding the
difficulties, however, Archimedes followed out his calculations
to the piling up of bewildering numbers, which the modern
mathematician finds to be the consistent outcome of the problem
he had set himself.
But it remains to notice the most interesting feature of this
document in which the calculation of the sand- grains is
contained. "It was known to me," says Archimedes, "that most
astronomers understand by the expression 'world' (universe) a
ball of which the centre is the middle point of the earth, and of
which the radius is a straight line between the centre of the
earth and the sun." Archimedes himself appears to accept this
opinion of the majority,--it at least serves as well as the
contrary hypothesis for the purpose of his calculation,--but he
goes on to say: "Aristarchus of Samos, in his writing against the
astronomers, seeks to establish the fact that the world is really
very different from this. He holds the opinion that the fixed
stars and the sun are immovable and that the earth revolves in a
circular line about the sun, the sun being at the centre of this
circle." This remarkable bit of testimony establishes beyond
question the position of Aristarchus of Samos as the Copernicus
of antiquity. We must make further inquiry as to the teachings of
the man who had gained such a remarkable insight into the true
system of the heavens.
ARISTARCHUS OF SAMOS, THE COPERNICUS OF ANTIQUITY
It appears that Aristarchus was a contemporary of Archimedes, but
the exact dates of his life are not known. He was actively
engaged in making astronomical observations in Samos somewhat
before the middle of the third century B.C.; in other words, just
at the time when the activities of the Alexandrian school were at
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